Stability and asymptotic behaviour of a two-dimensional differential system with delay

In this paper we study stability and asymptotic behaviour of a real two-dimensional system x (t ) = A(t)x(t ) + B(t)x(t − r) + h(t, x(t ), x(t − r)), where r > 0 is a constant delay, A, B and h being the matrix functions and the vector function, respectively. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Stability and asymptotic properties of this equation are studied by means of a suitable Lyapunov–Krasovskii functional.  2002 Elsevier Science (USA). All rights reserved